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Number 37. FIGURE 9.22 Problem 35 36. Wildlife biologists fire 20-g rubber bulle

ID: 1321667 • Letter: N

Question

Number 37.

FIGURE 9.22 Problem 35 36. Wildlife biologists fire 20-g rubber bullets to stop a rhinoceros charging at 0.81 m/s. The bullets strike the rhino and drop vertically to the ground. The biologists' gun fires 15 bullets second at 73 m/s, and it 14akes 34 s to stop the rhino. (a) What impulse does each bullet deliver? (b) What's the rhino's mass? Neglect forces between rhino and ground. 37. Consider a system of three equal-mass particles moving in a plane; their positions are given by a1 + bj, where ai and bi are functions of time with the units of position. Particle 1 has al = 3t2 + 5 and bi = 0; particle 2 has a2 = 7t + 2 and b, = 2; particle 3 has a3 = 3t and 1)3 = 2t + 6. Find the center-of-mass position, velocity, and acceleration of the system as functions of time. 38. You're with 19 other people on a boat at rest in frictionless water. The group's total mass is 1500 kg, and the boat's mass is .12,000 kg. The entire party walks the 6.5-m distance from bow to stern. How far does the boat move?

Explanation / Answer

For the 'i direction' for example, the component of the centre of mass's position vector is Rxi where:

Rx = (sum of (mass * magnitude of i-component)) / (sum of masses)
= (ma1 + ma2 + ma3) / 3m
= [(3t^2 + 5 ) + (7t + 2) + 3t]/3
= (3t^2 + 10t + 7) /3
= t^2 + 3.33t + 2.333

So the i-component of the position vector for the centre of mass is (t^2 + 3.33t + 2.333)i

The i-component of the centre of mass's velocity, vxi is found by differentiating w.r.t time
vx = dRx/dt = 2t+3.33

So the i-component of the velocity vector for the centre of mass is (2t + 3.33)i

Repeat for j and k.